Cognitive Molecular Communication Malcolm Egan, Trung Duong, Marco Di Renzo, Jean-Marie Gorce, Ido Nevat, Valeria Loscrì

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Malcolm Egan, Trung Duong, Marco Di Renzo, Jean-Marie Gorce, Ido Nevat, et al.. Cognitive Molecular Communication. 2018 -3rd Workshop on Molecular Communications, Apr 2018, Ghent, Belgium. pp.1-2. ￿hal-01728766￿

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Malcolm Egan, Trung Q. Duong, Marco Di Renzo, Jean-Marie Gorce, Ido Nevat and Valeria Loscri

Abstract—A key requirement of molecular communication to molecular communications. This leads to the notion of systems in many complex environments is that they should not cognitive molecular communications. disrupt the function of pre-existing biochemical systems; that is, In this paper, we develop the analogy between coexistence in the systems should coexist. In this paper, we develop a general framework for the coexistence problem by drawing an analogy to molecular communications and each of the three basic strate- the cognitive radio problem in wireless communication systems. gies in cognitive radio problem; namely overlay, underlay and For the particularly promising underlay strategy, we propose a interweaving. A key observation is that an important challenge formalization and outline key consequences. is to establish the impact of a molecular communication link on a biochemical system, particularly for the underlay strategy. I.INTRODUCTION To this end, we outline our proposal in [2] to address this Some of the most ambitious proposals for the use of molecu- challenge. lar communications are in complex environments, such as bio- chemical systems in the human body. In these environments, it II.COGNITIVE STRATEGIES is not only necessary for the molecular communciation system In cognitive radio, there are three basic strategies—underlay, to work reliably, but also for the biochemical system to retain overlay and interweaving—to allow a wireless network to its function. That is, the molecular communication system and access spectrum that has already been allocated to an existing the biochemical system can coexist. In order to achieve this, wireless network without significantly degrading performance the molecular communication system must be aware of its [3]. In this section, we propose that similar strategies are environment and be able to adapt its communication strategy. also available for the coexistence problem in molecular com- At present, a framework is not available to establish when a munications and identify scenarios where each strategy is molecular communication system and a biochemical system applicable. can coexist. A key difficulty is the fact that biochemical The basis for the analogy between cognitive radio and the systems are governed by reaction-diffusion dynamics. These molecular communications coexistence problem is that both dynamics are described by systems of differential equations, the molecular communication system and the biochemical which means that standard information and communication system exchange mass due to reactions between chemical theoretic tools are not straightforward to apply. As such, it is species in each system. They also exchange information, either challenging to determine the fundamental limits of the molec- through dedicated reaction pathways or indirectly through ular communication system subject to constraints imposed by observations made locally in the molecular communication the presence of the biochemical system. system. A similar situation occurs in cognitive radio, except Nevertheless, the general problem of coexistence in molec- instead of the exchange of matter, the interaction is through ular communication system bears strong analogies to coexis- electromagnetic interference. tence in wireless communications, which has been addressed The first strategy is underlay, where cooperation is not by the cognitive radio framework [1]. In cognitive radio, a possible but the molecular communication system has knowl- secondary wireless communication network aims to access edge of its impact on the biochemical system. The impact of spectrum that is licensed to a primary wireless network without the molecular communication system is determined by any degrading the performance of the primary network. An anal- changes to the dynamics of the biochemical system. More ogy between coexistence in molecular communications and precisely, this impact can be formalized as changes to initial cognitive radio is highly desirable due to the well-developed conditions or parameters of the differential equations describ- toolbox for cognitive radio. ing the reaction-diffusion dynamics of the biochemical system. In particular, in the problem of coexistence in molecular The underlay strategy is necessary when the information communications, it is possible to identify the biochemical molecules used for the molecular communication link either system with the primary network, while the molecular commu- overlap or react with the species in the biochemical system. nication link can be identified with the secondary network. As In the case where the biochemical system is complex—i.e., such, fundamental strategies in cognitive radio can be adapted containing a very large number of species—this situation is likely to occur and therefore it is important to design the M. Egan and J.-M. Gorce are with Univ. Lyon, INSA Lyon, INRIA, CITI, France (email:[email protected]). T.Q. Duong is with the Institute molecular communication link to ensure the concentration of Electronics, Communications and Information Technology in Queen’s of species in the biochemical system are not significantly University Belfast, UK. M. Di Renzo is with the Laboratoire des Signaux et perturbed. Systemes,´ CNRS, CentraleSupelec,´ Univ Paris Sud, Universite´ Paris-Saclay, France. I. Nevat is with TUM Create, Singapore. V. Loscri is with INRIA, The second strategy is overlay. In the context of cognitive France. radio, the overlay strategy is applicable when the secondary transmitting device has knowledge of the codebook and mes- Suppose that for the trajectory x(t) with initial conditions S sages of transmissions in the primary network. That is, a high x(0) ∈ (u + H) ∩ R≥0, the following limit holds level of side information is available to the secondary network. lim x(t) = α. (1) The analogous setting in molecular communications is when t→∞ the molecular communication link and the biochemical system Further, let (SI , RI , kI ) be the reaction system corresponding are jointly designed. to a molecular communication link. Suppose that reactions Such a joint design can be developed in biochemical systems involving species in S and SI are of the form regulated by DNA transcription. In particular, if the transcrip- X X X tion process is modified so that the production of information bjIj + cjXj  djXj, (2) molecules is a by-product of existing chemical reactions, then j j j there is no loss in the function of the biochemical system. where at least one element of each set {bj}, {cj}, {dj} is A key example of this situation occurs in bacteria colonies S strictly positive. Then, for any initial conditions u ∈ R>0, such as Vibrio fischeri or Vibrio herveyi, where a dedicated S there exists a unique equilibrium in (u + H) ∩ R≥0 given by communication link is established between bacteria, which is limt→∞ x(t) = α. supported by the production of autoinducer molecules during the DNA transcription process [4]. A key observation from Theorem 1 is that not all choices The third strategy is interweaving. In cognitive radio, this of information molecules will guarantee the stability of the strategy ensures that the secondary network does not interfere external biochemical system. The conditions in Theorem 1 with the primary network by detecting spectrum holes. That place constraints on the choice of information molecules. is, no side information assumptions are required at the cost In particular, the conditions suggest that the information of additional signal processing to detect whether there is a molecules should behave similarly to enzymes for chemicals primary network transmission on a given band at a given time. in the biochemical system. In molecular communications, the analogous situation is IV. CONCLUSIONS when the information molecules do not react with any species in the biochemical system. In this case the molecular commu- We have introduced the notion of cognitive molecular nication link can be viewed as an isolated chemical system, communications and identified an analogy with cognitive radio able to coexist with the biochemical system. This is an assump- in wireless communications. This reveals a number of design tion widely used in existing communication and information strategies to tackle the problem of coexistence in molecular theoretic studies, e.g., [5]. Nevertheless, it may be challenging communications and the important role of chemical reaction to implement unless the dynamics of the biochemical system network theory. However, there remain several open questions. are very slow. For instance, what insights can be obtained for more general reaction-diffusion networks? Another issue is how the molec- III.COEXISTENCEVIA UNDERLAY ular communication system can obtain information about the Due to its limited requirements, the underlay strategy is dynamics of the biochemical system. In particular, when is it particularly attractive. A key question in order to implement possible for the molecular communication system to adapt to underlay methods is how to characterize the impact of a the presence of new biochemical systems? molecular communication system on a biochemical system. REFERENCES At present, there is not a general answer to this question. Nevertheless for the class of reaction-limited systems [2], [6], [1] S. Haykin, “Cognitive radio: brain-empowered wireless communications,” IEEE Journal on Selected Areas in Communications, vol. 23, no. 2, we have recently proposed an approach based on chemical pp. 201–220, 2005. reaction networks. Formally, in order to model biochemical [2] M. Egan, T. Mai, T. Duong, and M. Di Renzo, “Coexistence in molecular systems as chemical reaction networks, the system is viewed communications,” Accepted for publication in Nano Communication Networks, 2018. as a tuple (S, R, k) consisting of a set of chemical species, [3] A. Goldsmith, S. Jafar, I. Maric, and S. Srinivasa, “Breaking spectrum denoted by S, that are related by a set of chemical reactions, gridlock with cognitive radios: an information theoretic perspective,” denoted by R, occuring at rates governed by a rate function Proceedings of the IEEE, vol. 97, no. 5, pp. 894–914, 2009. [4] M. Miller and B. Bassler, “Quorum sensing in bacteria,” Annu. Rev. k. As such, the building blocks are the chemical species in Microbio., vol. 55, pp. 165–199, 2001. the system and the possible reactions between each subset of [5] K. Srinivas, A. Eckford, and R. Adve, “Molecular communication in fluid species. media: the additive inverse Gaussian noise channel,” IEEE Transactions on Information Theory, vol. 58, no. 7, pp. 4678–4692, 2012. Under mass action kinetics [7] and certain conditions on the [6] M. Egan, T. Mai, T. Duong, and M. Di Renzo, “Coordination via biochemical system that guarantee the existence of a unique advection dynamics in nanonetworks with molecular communication,” in equilibrium, we have established the following result. For full Proc. IEEE International Conference on Communications (ICC), 2018. [7] M. Feinberg, “Chemical reaction network structure and the stability of details, see [2]. complex isothermal reactors–i. the deficiency zero and deficiency one theorems,” Chemical Engineering Science, vol. 42, no. 10, pp. 2229– Theorem 1. Let (S, R, k) be a weakly reversible complex 2268, 1987. balanced reaction system with point of complex balance α.